Forgive my last post, I guess there must be a way to do it with algebra ... the hard way.
Forgive also what I said in this post, lol, I must be tired.
As mathaddict said, try to multiply the equations to get rid of the fractions and revert back to the good old quadratic equation. It makes it a lot easier.

If a line is a tangent to the curve , it touches the curve at one point .

so

calculate the value of m , then put this value of m into ** , evaluate the x-coordinate then .

for (2) , you are given the range , so

compared this with , ?? (i think you have a typo here)

we see that c=2 , d=15 assuming that i guess it correctly .

yes sorry for my typo. Well, thanks and I understood part a fully. About part b, it is about turning the x values into equation and then expanding and comparing to find c and d... it just seems so much like any other quadratic equations thanks

(a)Find the value of m for which the line is a tangent to the curve and find the x-coordinate of the point at which this tangent touches the curve.

(b) Find the value of c and of d for which is the solution set of

For (a), how do I actually solve the quadratic equation when the equation have a ?

What quadratic equation are you talking about? There is no quadratic equation here. A line crosses a graph if the equation of the line and the equation of the graph have a common factor- that is, if . The line is tangent to the curve if that is a double root. To get a quadratic equation, multiply both sides of the equation by x.

For (b), start by finding solutions to the equation. Those two points must separate "<" from ">". Try a single point, say x= 0, to determine which is which.